In the application of evolutionary algorithms to real world problems, the full black-box view of the fitness function (ignoring all additional information about its inner workings) is at most the initial prototype;
significant improvements can be made by applying problem knowledge for designing tailored variation operators [1]}.
The resulting view is called gray-box optimization, and research tries to understand what general structural properties can be usefully employed in evolutionary computation [2]}.
We are interested in combinatorial problems where a certain subset has to be selected; typically, the number of elements in the chosen set is rather important.
For example, a minimum spanning tree contains exactly \(n-1\)  edges, the vertex cover problem tries to minimize the number of vertices picked, and the independent set problem maximizes the selected vertices.
While [3]} argued that variation operators should be unbiased with respect to whether a 0 or a 1 encodes a specific property of a solution, the gray-box view of combinatorial problems wants the 1 to mean `in' and 0 to mean `out', and then design operators that can make use of this meaning.
From the very general work of Rowe and Vose [4]} we can see that only for problems which have symmetrical meaning in 1 and 0 can the operators be assumed unbiased.
